Question

Rationalise the denominator root 2+root 3/3 root 2 -2root3 ,a-b root6

Answer 1

Heya !!!



✓2 + ✓3 / 3✓2 - 2✓3 = A - B✓6


LHS = ✓2 + ✓3 / 3✓2 - 2✓3



Rationalizing the denominator 3✓2 - 2✓3



=> ✓2 + ✓3 / 3✓2 - 2✓3 × 3✓2 + 2✓3 / 3✓2 + 2✓3



=> ( ✓2 + ✓3) ( 3✓2 + 2✓3 ) / ( 3✓2 - 2✓3 ) ( 3✓2 + 2✓3)



=> ✓2 ( 3✓2 + 2✓3 ) + ✓3 ( 3✓2 + 2✓3) / ( 3✓2)² - (2✓3)²


=> 6 + 2 ✓6 + 3✓6 + 6 / 18 - 12



=> 12 + 5✓6 / 6


Now,



LHS = RHS


12 + 5✓6 / 6 = A - B✓6


Clearly,



A = 12/6 = 2 and B = 5/6




HOPE IT WILL HELP YOU....... :-)

Answer 2

$\frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \\ \\ by \: rationalization \\ \\ \frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } \\ \\ \frac{( \sqrt{2} + \sqrt{3} )(3 \sqrt{2} + 2 \sqrt{3}) }{ {(3 \sqrt{2} )}^{2} - {(2 \sqrt{3} )}^{2} } \\ \\ \frac{6 + 2 \sqrt{6} + 3 \sqrt{6} + 6 }{18 - 12} \\ \\ \frac{12 + 5 \sqrt{6} }{6} \\ \\ \frac{ (12 +5 \sqrt{6} )}{6} \\ \\ 2 +5 \sqrt{6}$

2 + 5√6 = a - b√6

a = 2
-b = 5
b = -5

=================
a = 2

b = -5/6

I hope this this will help you.

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